PDS — A Three-Dimensional Data Structure for Proof Plans

We present a new data structure that enables to store three-dimensional proof objects in a proof development environment. The aim is to handle calculus level proofs as well as abstract proof plans together with information of their correspondences in a single structure. This enables not only different means of the proof development environment (e.g., rule- and tactic-based theorem proving, or proof planning) to act directly on the same proof object but it also allows for easy presentation of proofs on different levels of abstraction. However, the three-dimensional structure requires adjustment of the regular techniques for addition and deletion of proof lines and backtracking of the proof planner.